Nov., 1937
AT HIGHDENSITY P-V-T PROPERTIES OF NITROGEN
3. An equation of state has been fitted to the data of this paper and to all other available data on nitrogen between -45 and -208' a t densities from 210 to 750 Amagat units. 4. The Joule-Thomson inversion curve for nitrogen has been calculated from the equation
[CONTRIBUTION FROM THE
2233
of state and found to agree with the experimental curve of Roebuck and Osterberg. 5. The density of nitrogen a t 0' and 1550 atm. has been determined as a reference datum for further work a t higher pressures. CAMBRIDGE,
MASS.
RECEIVED JULY 26, 1937
RESEARCH LABORATORY OF PHYSICS, HARVARD UNIVERSITY]
Pressure, Volume, Temperature Properties of Nitrogen at High Density. 11. Results Obtained by a Piston Displacement Method BY MANSON BEN EDICT^
Introduction The first paper* of this series, hereafter to be referred to as I, described a gravimetric method for determining the density of nitrogen most suitable a t densities greater than 200 A. u. (Amagat units) and pressures less than 1550 atm. Density a t 1550 atm. and 0' was determined with special care for use as reference point for measurements at higher pressure. The present paper describes a piston displacement method for determining density, relative to this reference point, a t pressures between 1000 and 6000 atm. and temperatures between -175 and $200'. In 1923 Bridgman3used this general method with kerosene as a pressure transmitting fluid to determine the isothermal compressions of five gases a t pressures up to 15,000 atm. and a t temperatures around 65'. The extreme pressure range there studied yielded much valuable information, but inevitably diminished the precision attainable, principally because of erratic volume changes in the pressure chamber. More recently he4 designed an apparatus employing the gas itself as pressure transmitting fluid and used it to determine the freezing curves of nitrogen and argon. At the same time he determined the thermal expansion at constant pressure of these gases from 68' to lower temperatures a t several points in the pressure range 3000-6000 atm. These recent data and the less precise earlier isothermal data served to outline roughly the P- V-T surface of these gases at high pressures. At Professor Bridgman's suggestion the writer undertook a more complete study of the P-V-T properties of nitrogen with the same (1) National Research Fellow in Chemistry, 1935-1936. JOURNAL, 09, 2224 (1937). (2) Benedict, THIS (3) Bridgman, Proc. A m . Acad. Arts Sci., 69, 173 (1924). (4) Bridgman, ibid., TO, 1 (1935).
apparatus. Isothermal compression, as well as isobaric thermal expansion, has been determined, so that dependence on the earlier isothermal data has been avoided. Though the pressure range was limited to 6000 atm., it was possible to extend the temperature range and to attain results estimated accurate to 0.3% on the density.
Experimental Survey of Method.-A diagram of the apparatus is shown in Fig. 1. Bridgman's4 paper describes its construction in detail. Paper I describes the nitrogen used and experimental procedure not explicitly mentioned here. The apparatus consisted essentially of three parts, the upper cylinder A in which the gas was compressed at 25" and its volume change measured, the lower cylinder B, exposed to any temperature to be studied, and the connecting pipe C. For each loading of gas the moving plug M was brought to the top of the upper cylinder and nitrogen precompressed to 900 atm. or more was admitted a t G. Pressure of gas in A was indicated by resistance of the manganin gage D. With gas in A, B, and C a t the reference temperature, 25', the gas-tight moving plug M was advanced by the piston until it had isolated this gas from the precompressors and compressed it to the reference pressure, 1566 atm. With A a t 25" and B, successively, a t each temperature to be studied, the displacement of M required to produce each pressure of interest was determined. At the conclusion of a specific cycle of pressure and temperature changes, a blank run was made to eliminate from consideration the unknown total volume of A, B, and C and their incalculable stretch with pressure. In this blank run, iron blanks 41and 42 were placed in A and B, respectively, and the new positions of M required for the same cycle of pressure and temperature changes were determined. Then it was possible to express the ratio of the volume of gas a t any temperature and pressure studied to its volume a t 25" and 1566 atm. in terms of the positions of M observed in the blank and gas-filled runs, the area of A, and the known volumes of 41 and 42. Terminology.-The two properties of the gas most directly obtainable from the observed positions of the moving plug are the isothermal compression and isobaric
3234
MANSON BENEDICT
thermel expansion. If V(t, P) is the volume of a given mass of nitrogen at t o and P a b . , then we will define K the isothermal compression by (1) V(25, P) V(25,1566) I(= (1) V(25, 1566)
-
and B the isobaric thermal expansion by (2) V(t,P) V(25, P) = V(25, P)
'
-
Temperature Measurement.-Q was the cryostat described in I. A less sensitiye method of temperature control was employed here; the heat input required t o maintain constant temperature was actuated by a hydrogenmercury thermoregulator and thyratron relay. This scheme produced temperature oscillations of period one minute, magnitude 0.25'. Cryostat temperature, tz.
VOl. 59
t o 0.1' by the Bureau of Standards for all temperatures a t which we used it. Proper emergent stem corrections were applied, so that the temperature of B at and above 25' was known withim 0.1'. Temperature tl of the unthermostated kerosene bath R surrounding the upper cylinder was measured with a copper constantan thermocouple touching the upper cylinder A. This thermocouple was compared with a calibrated mercury thermometer in the temperature range of interest. Its temperature drifted slowly with changes in room temperature from 22.5 to 27.5'. Temperature of the gas in the upper cylinder probably differed from that indicated by the thermocouple by less than 0.2' for the small rates of temperature change observed of the latter. All gas above liquid level in Q was supposed to have been at tl; all below it, at tz. Pressure Measurement.-DetaiIs of pressure measuring equipment are given in I. Manganin resistance gage 2 was used t o measure pressure in the experiments a t low temperatures, and gage 5 was used in experiments above room temperature. Gage 2 was compared up to 6000 atm. with standard gage A, previously calibrated against the freezing pressure of mercury at 0". Resistance change with pressure of gage 2 was proportional t o that of the standard gage within a probable error of 0.16%. Unfortunately, both gage 2 and standard gage A were broken before they could be campared with the free piston gage. The comparison of gage 5 with standard gage B and with a free piston gage was described in I. Gages 2 and 5 had been wound from the same spool of American manganin and their values of a differed by only 0.14%. Gages A and B had been wound from the spool of German wire which Bridgman used in his original determination of the freezing pressure of mercury, and their values of Q differed by only 0.01%. In view of this similarity in each pair of gages, we have supposed gages 2 and A t o read the same pressure scale as gages 5 and B. We have therefore used eq. (4) of I t o correct the pressure Pm read by gage 2 to the absolute pressure P. We estimate the maximum error in P thus calculated for gage 2 t o be 0.3%.
Dimensions of Apparatus and Measurement of Volume. (a) Upper Cylinder.-The over-all length of the reamed hole in the upper cylinder was 8.5 cm.,and its mean area at 1atm. pressure, Ao, was 0.3462 an.* The position of moving plug M in the cylinder was determined by observing the position of steel wire W relative to glass Fig. 1.-The apparatus. scale S with a vertical travelling microscope. was measured by the four junction copper-constantan Nominal sensitivity of the micrometer moving the thermocouple described in I. Temperature of B was thus latter was 0.0005 cm. The scale was ruled at known within 0.3" below 0'. For measurements of thermal expansion between 25' and higher temperatures, Q 0.05-cm. intervals. Each ruling was compared was a s m d oil-bath with stirring mechanism of the type with a standard meter bar ruled at 0.02-cm. described by Collins;6 its temperature was controlled by a intervals and checked at the U. S. Bureau of "Hytemco" resistance thermometer, A. C. bridge, ampli- Standards. Positions of M were referred to a fier, and phase shifting thyratron circuit as described elsebench mark 1.63 cm. below the top of the cylinwhere.' Bath temperature was read with a mercuryin-glass thermometer graduated in 0.5" and calibrated der. The working range of the plug was between the bench mark and a position 4.7 cm. lower. ( 5 ) Collins, Rev. Sci. Insfrztmcnls, 7, 502 (1936). Total volume displaced was 1.63 cc. The clear(6) Benedict, ibid., 8, 252 (1937).
P-V-T
Nov., 1937
PROPERTIES OF NITROGENAT HIGHDENSITY
ance at each end of the cylinder was sufficient to avoid end effects in the stretch of the cylinder under pressure. Hence, eq. (5) of I can be used to estimate the increase of do with pressure, provided AA and 0.3462 be substituted therein for AV9 and V. For steel E = 2.1 X lo8 atm. u = 0.3, and rl = 2.54 cm. r2 = 0.332 cm. so that A = 0.3462 4.2 X 10-’Patm.
+
The change of A with pressure may be in error by 20% because of uncertainty in the theory of the elastic distortion of thick-walled cylinders. The diameter of the reamed hole in A was determined a t 0.5-cm. intervals over the working range by means of a special internal micrometer working on the principle of the star gage used to check the bore of guns.’ The micrometer was checked against gage blocks with a probable error of 0.0003 cm. The reamed hole was circular within this tolerance and varied with elevation between 0.6621 and 0.6670 cm. At the end of the experiments the diameter was redetermined a t one elevation and was found to have decreased by 0.0004 cm. Hence, no sensible permanent deformation of the upper cylinder took place. The irregularity in bore was allowed for by including the correction for it with the correction for errors in ruling of the glass scale. The largest correction for irregularity in bore corresponded to 0.010 cm. plug displacement. Errors in measurement of linear displacement and bore and in estimation of stretch produce an estimated maximum error of 0.3% in the volume displaced by the moving PlugVolume contained by the connecting pipe and upper cylinder with M at the bench mark was determined with a gas buret as described in I. Volume contained by C was 0.151 ml., estimated from its length, 12” (30.7 cm.) and its inside diameter, l/34’’ (0.8 mm.). VI, the volume contained by A with M at the bench mark and upper 9’ (23 cm.) of C, was 2.59 * 0.005 ml. A rough estimate of this volume is required in correcting for variations of tl from 25’. The volume of B was approximately 1.2 ml. (b) Iron Blanks.-The iron blanks were cut from the block of Armco iron used by Bridgman8 (7) See, for instance, W. H. Tschappat, “Ordnance and Gunnery,” John Wiley and Sons, Inc., New York, 1917, p. 283. ( 8 ) Bridgman, PYOC. A m . Acad. Avts Sci., 68, 169 (1923); 70,
a12 (1935).
2235
for measurements of its absolute compressibility. They were turned to right circular cylinders and polished. The length and diameter of each was measured by micrometer calipers checked against gage blocks. Their volumes at 25’ and 1 atm. were 4: = 1.492 * 0.001 ml. and &’ = 1.187 * 0.001 ml. At centigrade temperature t 2 and pressure P a t m . the volume of either blank, + p l , was calculated from its volume a t 25’ and 0 atm., 4O, by eq. (3).
+ -
+
+
= +“(1 6.05 X 1O-’P 2.5 X 10-”P2 l35.4 e 20.6 e 2 10.1 ea 3.5 e*]) e = 0.001 ( k 25)
&pt
10-8
-
+
(3)
This equation is based on the “International Critical table^"^ formula for the linear expansion of iron above 0’ and on Bridgman’s value for the compressibility of iron a t 30’. The change of compressibility with temperature is neglected. The “I. C. T.” formula agrees well with Henning’sg value for the mean linear expansion of iron between -190 and 20’. Use of eq. (3) to calculate the volume of iron under the conditions of these measurements probably introduces no error greater than 0.05’%. It is impossible to calculate the changes with pressure and temperature of the internal volume of the apparatus because of stretch in the packed connections. Also, 0.15 ml. of gas in connecting pipe C is exposed to an unknown temperature gradient. The effect of these two uncertainties was eliminated by the runs in which B was totally and A was partially filled with the iron blanks whose volume change with temperature and pressure was small and known with sufficient accuracy. Successful application of this method is based on the assumptions that the volume contained by the apparatus responds reproducibly to a given cycle of pressure and temperature changes, and that the temperature gradient in C is reasonably reproducible. If these conditions are fuliilled, the only volumes of nitrogen which enter the calculations of the compression and thermal expansion are those displaced by the moving plug in either run or replaced by the iron in the blank run. (c) Possible Sources of Error.-There were a number of possible sources of error which needed consideration. Temperature gradient in C was made as definite as possible by maintaining thermostat liquid level constant within 1 cm. The four packed connections, shown black in (9) “International Critical Tables,” Vol. 11, p. 460.
2236
MANSON BENEDICT
Fig. 1, were possible sources of erratic volume changes. Of them the two around the connecting pipe were lead and probably responded reproducibly to pressure and temperature change. The lower connection was broken each time & was put into or taken from the lower cylinder, Judging from the agreement of results for density change from 25' calculated from gas-filled runs made before and after a blank run, the volume of the lower cylinder could be satisfactorily reestablished within 0.3y0each time this connection was made. However, some increase in volume of the apparatus gradually took place, because calculation of the compression by combining blank and gas-filled runs separated by many intermediate applications of pressure gave erratic results. This increase in volume was probably caused by extrusion of the soft rubber packing around the resistance gage electrode. Its effect was rendered unimportant by calculating the compression from consecutive blank and gas-filled runs a t 25'. Change in the total volume of the upper cylinder between a blank and gas-filled run does not affect the thermal expansion calculated from them. One troublesome scurce of volume change in the first three runs was gradual accumulation in the upper cylinder during a run of as much as 0.015 cc. of the soft rubber packing from around the moving plug. A t the end of each run the packing was recovered and weighed and the observed positions of the moving plug were corrected for its presence by assuming that in a run in which n forward strokes of the piston were taken, one nth of the total volume of packing recovered was left within the cylinder after each stroke. After run 4, brass retaining rings were used on the moving plug, and the amount of packing accumulating was unimportant. Unless an audible leak had occurred, the apparent loss of gas during a run due to penetration of gas through the steel, slow leak, or permanent deformation of the apparatus never exceeded 0.005 cc. measured a t 1566 atm. and 25'. Hence, only those runs in which an audible leak occurred were rejected. Volume hysteresis with respect to pressure change was reproducible and, in the extreme pres sure range, amounted to 0.012 cc. Since observations customarily were made on decreasing pressure only, it was important to establish that the hysteresis was got in the bore of the upper
VOI.
59
cylinder or in the iron blanks. If it occurred elsewhere, it was of no importance since it was reproducible. Accordingly, blank and gas-filled isotherms were run at 25' on both increasing and decreasing pressures. The average difference in the volume observed a t ten pressures increasing from 1566 to 5800 atm. from the volume observed a t the same pressures in reverse order was $0.06%. The difference is within the probable error of volume measurement. Reduction of Data.-The primary data from a single loading of gas consisted of a set of points a t each of which were measured y, the distance of M below the bench mark; t l , the temperature of the upper cylinder; tz, the temperature of the lower cylinder; and P, the pressure, each calculated from the calibration of the appropriate measuring instrument. The data had to be taken quickly because of the short life of gas-tight packing a t high pressure. I n the time available tz was not brought exactly to the even temperature desired, but differed from it on the average by 0.5', and P differed from the desired pressure by 5 atm., on the average. If p' be l/V(dV/dt). for nitrogen a t 25' and P atm., Sy, the correction to be added to y for the departure of 11 from 25' was calculated by (4). B' was calculated from the eq. of state (12), to be given later. k~ = P'( VdAo - ~ ) ( h- 25) (4) y was next corrected to the value it would have had at the desired value of P by interpolation between adjacent points with respect to log P, on which y was roughly linearly dependent. Finally, y was corrected to the value it would have had a t the desired value of tz by linear interpolation between adjacent temperatures. It is to be noted that these adjustments preserve any error in y and do not smooth it. The isothermal compression was calculated from corresponding positions of the moving plug in a blank and a gas-filled run at 25' as follows: In the gas-filled run, suppose the moving plug is initially Yoocm. below the bench mark a t 1566 atm. and after a specific cycle of pressure changes suppose it is Yp, cm.below a t P. Then suppose the internal volume of the apparatus reduced in the blank run by the addition of iron having a volume &I at 1566 atm. and 4 p at P and 25'. Suppose the piston position in the blank run is yooa t 1566 atm. before the same cycle of pressure changes and ypo at P after it. Let do and A P be the internal areas of the upper cylinder and
P-V-T PROPERTIES OF NITROGEN AT HIGHDENSITY
Nov., 193'7
Uo and Up the total internal volumes of the apparatus (withy = 0) at 1566 and P atm. respectively. We can express the conservation of gas by (Uo - AoYoo)/V(25, 1566) = ( U p - ApYpJ/V(25, P)
TABLE I PRESSUREAND TEMPERATURE RANGE OF RUNS Run 1
(5)
in the gas-filled run and (uo - 60- Aoyoo)/v(25,1566)
=
( U P- +P
-
A P Y P J / V ( ~P) ~,
in the blank run. The unknown volumes UOand U p may be eliminated
The equation for calculating the thermal expansion, & from positions of the moving plug in gas-filled and blank runs is derived analogously. In the gas-filled run after a given cycle of pressure changes, suppose the moving plug is a t U p , when B is a t 25' and pressure is P. After a further cycle of pressure and temperature changes, suppose the plug is a t Up, when B is a t t; and the pressure is again P. Then suppose iron blank $2 is placed in the lower cylinder and the cycle of pressure and temperature change is repeated, yielding corresponding plug positions ypo and ypl.. If the volume of the iron blank is 4poa t P and 25' and $Pr a t P and t2, we obtain for p u t , P) 4Pt -U25, P) - -I- = 4 p 0 AP(YP" Y P ~ Y P ~- YP,)
2237
PresIron Mang. sure blanks gage Range
..
2
1550
B1
9r
to
Bla
@a
5850
B2 2 3 B3 4 5 8 B4
41
91
to
B4a
$1
5850
B5 9 10 10a
11
+
..
atm.
+#
*.
2
914-9r
..
.. ..
atm.
+ 91 + 92 91 + 99 ..
.. .. ..
C.
;,"" {
3400 5
Order of isotherms,
25 0 -125 -100 -75 -45 25 25 25 25 0 -125 -100 -75 -45 23 25 0 -125 -100 -75 -45 25 25 0 -175 -150 -125 -100 -75 -45 25 25 as in 3 and B3 25 25 50 100 150 25 25 200 25 26 150 100 50 25 25 25 150 100 50 25 25 200 25 25 50 100 150 25
1260 atm.
}
The 2 5 " Isotherm-To minimize the influence of the gradual volume change in the packing around the resistance gage electrode, the isothermal compression at 25' was calculated from consecutive 25' isotherms only. The isothermal compression calculated from all possible consecutive 25' isotherms was averaged and represented by eq. (8). K
+ 1 = V(25, P)/V(25, 1566) = 1 . 8 6 6 6 ~1 . 6 0 7 9f ~ ~0 . 9 1 6 5 ~x~ ;=
41oOo/P
(8)
Eight independent combinations of consecutive runs were used in calculating K 1; the devia( 7) tion plot for 25' in Fig. 2 illustrates the scattering V(t,P)/V(25, 1566) was not calculated directly a t the individual points. The root mean square from blank and gas-filled runs because correspond- deviation of the averaged observed volumes from ing runs were sometimes separated by several the calculated volumes a t 25' was 0.04%. The applications of pressure or by necessary repairs to root mean square deviation of the individual obthe upper cylinder. Each of these would intro- served volumes from the averaged observed volduce possible volume changes in the upper cylinder umes was 0.27%. and consequent uncertainties in the calculation of Reference to Table I will show that about as isothermal compression, though not in the cal- many gas-filled runs precede the associated blank culation of isobaric thermal expansion. run as follow it. This should disclose the magnitude of systematic error due to gradual increase in Results volume contained by the apparatus. Table I The Measurements.-Three series of measure- will show also the variety of blank runs used to ments were required to cover the temperature eliminate the unknown volumes and stretch of the and pressure range discussed in this paper. apparatus. The agreement of the various resiilts They are summarized in Table I. Runs Bla, for the compression indicates the degree of trustB4a and 10a were made without repacking any- worthiness of this method. In the different thing after the preceding runs. Otherwise, the combinations of blank and gas-filled runs, the moving plug was repacked after each run and the area of the upper cylinder and the volumes of the connection a t the lower end of C was broken wheii iron blanks enter the calculation of the compresriecessary to insert or remove $2. The electrode sion with differing weights; iii ail extreme i i i of the resistance gage was repacked after ruiis 4 and stance, runs B1 a i d B la, the volume of 41 and ~$2 5 . Between B1 and B l a about one-third of the do not eriter eq. (6) a t all. Hence, i t is reasongas originally present in the apparatus was released. able to take the root mean square error of the 25'
+
+
+
MANSON BENEDICT
2238
VOl. 59
from corresponding blank and gas-filled runs by means of eq. (7). These observed thermal expansions were combined with the mean observed values of K to convert them to isobaric volume change relative to the volume a t 25' and 1566 atm. That is /3(l K ) = [V(t,P) - V(25, P ) ] / V ( 2 5 ,1566) (9) Eq. (10) was fitted to the mean observed value of P(1 K ) by the method of least squares,
+
I
+0.2%
-
-0.2%
-
-~ -
J
?
*
a
e
I
a e 4
+
j2000 P(K
+ 1)
-
-
~[O.O003176(T T') 2.4511(1/fi - 1/47)] ~ ~ [ - 0 . 0 0 1 0 3 1 5 ( T- T')] ~'[0.0031237(T - T ' ) 4.4620(1/d/T 1,'dF)- 3.2661(1/T - l/T')] (10) x = vlOOO/P; T = t 273.2; T' = 298.2'K. =
+
+ +
-
+
]lrn0 100"
4
3, B3 8 4, B3 Z 5, B3 B 8, B4 @ 9, B5 0 10, B5 3 loa, B4a 3 11, B4 @
+0.2%k4
-0.2%
I
2
I
I
1 \ 1j j
I
The deviations of the observed volume changes from those calculated by eq. (10) are illustrated by the deviation plots of Fig. 2 for temperatures other than 25'. The root mean square deviation of the average observed volume changes from those calculated by (10) was 0.14 % of the total volume and the root mean square deviation of the individual observed volumes from their average was 0.17%. 0.17% is a measure of the effect of errors of observation, fluctuations in temperature gradient in C, and erratic volume changes taking place in the apparatus during a run. In order to express V(t, P) in Amagat K) units, eq. (8) was substituted for (1 in eq. (10); from this V(Oo,1550)/'v(25, 1566) = 0.9669. In I V(O', 1550) was found to be 1/558.5 A. u. Hence
+
-75O
V(2jo, 1566) = 0.0018518 A.
11.
(11)
With this datum, mean observed values of(1 p)(l K) were converted to - 1 2 ~ density ~ in Amagat units in Table 11. The average probable error in these densities is estimated to be 0.24% from -1500 the average root mean square errors in (1 K ) and (1 p)(l K ) , 0.27 and - 1750 0.17%, respectively, and the probable error in V(0, 1566), 0.09%. The probable error a t temperatures near 25' and 1 2 3 4 5 6 pressures near 1566 atm. is less than at Pressure, atm. X 103. points further removed. Big. 2 -- Dev. plot of individual observed volutncs. Equation of State.-By combining eqs. ( 8 ) , (10) and (11) the equation of state (12) Other Temperatures,-At temperatures other was obtained. This equation is than 25' the thermal expansion p was calculated
+
+
+
+
+
P- V-2" PROPERTIES OF NITROGEN AT HIGH DENSITY
Nov., 1937 103V = (3.54842 8.2630/d/T
+
-
O.UOO588lT 6.O483/T)x8
-
+ 0.0019102T)~~+ (-0.48596 = q m ; T = t("C.) + 273.2
4.6131/.\r)~ -(2.40797
x
valid overthe temperature range -175 to +200° and the pressure range 980-5800 atm. V is volume in Amagat units, and P is in atmospheres.
Temp.,OC. Press., atm. 981 1250 1566 1955 2442 2927 3413 3898 4382 4866 5351 5835
2.239
713.3 732.7 754.2
F R E
E 2
E S
672.2 695.1 721.5 744.6 768.7 794.1 813.7
631.8 661.2 688.9 714.9 742.3 767.1 787.5 805.1 821.3 838.1 8rj2.4
-
596.2 563.1 627.7 597 * 5 658.1 631.1 687.5 662.3 718.2 693.3 744.1 720.8 766.4 743.8 784.7 762.5 801.5 784.2 818.8 800.7 833.8 815.7 847.5 831.4
Discussion of Results The deviation plot, Fig. 3, illustrates the agreement between the P-V-T data of this paper, summarized by eq. (12), and all other existent data for nitrogen above 1000 atrn. The disagreement of 0.5% with Bartlett'sl" points a t 1000 atm. and -50 and -io" has been mentioned in I. It will be seen that this disagreement persists up to 2 5 O , but at higher temperatures the agreement is satisfactory. The present data differ from those of Amagat" and of Michels12 in that nitrogen appears to be 2y0more compressible, but the agreement of the volumes a t all but six of the points is within o.30/0, our estimated probable error. Bridgman's3 results a t 68" differ from eq. (12) by about lyo,on the average, and he finds nitrogen about 12% less compressible; this discrepancy is probably within his rather large experimental error. His points a t lower temperatures4 are not shown because they were based on his 68" isotherm and show the same general trend with pressure. Basset and Dupinay's13 volumes at 16' are seen to be about 3'% smaller than those of any other investigator. Equation (12) follows the trends of the P-V-T data sufficiently well to permit its use in evaluat(10) Bartletl, el d ,THTRJOURNAI., 49, 687, 1455 (1927); 62, :l i 4 (1930). ( 1 1) "International Critical Tables," Vol. 111, p. 17. (12) Michels, Wouters and de Boer, Physica, 3, 585 (1936). (13) Basset and Dupinay, Compl. rend., 191, 1295 (1931).
(12)
ing derivatives of I/ with respect to T and P (estimated accurate to 2%), and in extrapolating the volume somewhat beyond the measured
TABLE I1 MEANOBSERVED DENSITIESOF NITROGEN IN AMAGAT UNITS -45 0 25 50 125 - 100 75 - 175 -150
-
4- 0.0057846T f
526.1 563.9 600.5 633.8 668.2 698.6 721.1 742.1 763.0 780.3 796.0 811.9
479.3 521.4 560.5 598.3 635.4 666.8 692.6 714.7 736.1 753.5 771.0 785.0
456.1 499.4 540.0 578.9 616.9 648.9 676.1 699.5 721.0 740.1 757.2 773.6
100
150
200
477.4 443.5 411.7 520.7 486.6 456.3 560.7 529.3 501.0 600.0 571.4 543.8 632.2 604.4 579.2 661.0 633.5 609.6 686.6 658.7 634.3 709.0 681.6 659.0 727.2 702.4 679.8 744.7 722.1 700.7 762.1 738.5 717.4
429.5 473.9 517.8 554.8 584.9 612.5 634.8 658.6 678.1 698.2
temperature and pressure range. Several iiiteresting consequences of eq. (12) may be noted.
,b-I -
H
-0.6
-
1
2 3 Pressure, atm. X 103. 1 2 3 4 5 6
3 e
8
>
I Basset
& Dupinay
16'
0
+o.2
'
-0.2
r
~
'
-100
, ~
L
r,
c
I
11 -1-
l-
I
8
Bartlett, et al 1000 atm
0
100 200 Temperature, " C . Fig. 3.-Dev. plot for others' obs. volumes.
Isobars of V against T have positive curvature below about 1800 atm. and negative above that pressure. This is illustrated in Fig. 4 which shows the isobars calculated froni (12) a t even thousands of atmospheres. Since ( d C p / d P ) T =
MANSON BENEDICT
2240
- T(b2V/bT2)p,C p will have a minimum a t each temperature where the isobars have no curvature. The pressures a t which Cp is a minimum are givenin Table 111, 0.0030
0.0025
.-+dE a
3 0.0020
It will be noted that eq. (12) predicts that V will approach zero as the pressure increases indefinitely. This is opposed to the van der Waals model of the molecule as a rigid attracting sphere, but is consistent with the contemporary notion of the existence of a finite potential energy for every intermolecular distance. Some properties of nitrogen a t 30' above 1000 atm. are compared with those of an ideal gas in Fig. 5 . Each dimensionless quantity shown there equals 1 for an ideal gas. Although PV/RT increases seven fold over its ideal value, (bV/ bT)pP/R and - (3 V/bP),P2/RT remain much nearer unity.
7 L
I
E
.C
VOl. 59
/ / / 0.0010
l!
I -100 0 100 Temp., "C. Fig. 4.-Isobars of nitrogen.
200
Equation (12) has also been used to calculate temperatures and pressures a t the inversion points for the Joule free expansion effect a t which the "internal pressure," ( b U / d V ) , = 0 and the energy U is a minimum. When (bU/dV)T = 0, T ( bV/dT)p P(bV/bP)T= 0. The coordinates of the Joule inversion curve a t several temperatures are also given in Table 111. Density on this curve runs from 600.9 A. u. a t 200' to 807.i This is in qualitative agreeA. u. a t -150'. ment with the findings of Michel, Wouters, and de Boer;14 a t 150' their curve for (bU/bP)* extrapolates to 0 a t about 600 A. u.
--RT BP 1000 2000 3000 4000 5000 Pressure, atrn. Fig. 5.-Comparison with ideal gas a t 30'.
An interesting consequence of the trend of (bV/bT)pwith increasing pressure is that J ( b S / bP)TdP = - J ( b V / d T ) p d P decreases without limit, and at sufficiently high pressure S, the entropy, would become negative, in violation of the third law of thermodynamics. This paradoxical situation is relieved by the fact that nitrogen freezes a t very high pressures, and the properties of the solid phase presumably will not allow S to become negative. For instance, a t 0' nitrogen freezes a t about 20,000 atm.; a t this pressure the entropy has decreased from its value of TABLE 111 INVERSION POINTSFOR (dU/dV), AND (dCp/dP)T 45.2 cal./OC. mole at 1atm.I6to 21.3 cal./'C. mole. I t was possible to determine the freezing presPressure ( a t m ) at which T y p C. (D7'ldV)T = 0 (dCP/dP)T = 0 sures of nitrogen a t - 125, -- 150, and - 1 7 5 O . 200 :w5 2082 These were 5708, 367:3, and 1930 atm., resper100 3f34 304s lively. The agreement with Bridgmaii's4freezing 0 :
